Advected constant-volume porous gravity current
= Advected constant-volume porous gravity current
{title2=$h=[R^2-(x-ut)^2]_+/(6at)$}
An instantaneous point release of actual volume $V$ per unit width in a <porous gravity current with background flow> has the <Barenblatt solution> $h=[R(t)^2-(x-ut)^2]_+/(6at)$, where $R^3=9aVt/(2\phi)$. Its centre translates at pore speed $u=U/\phi$ and its radius grows as $t^{1/3}$. The conserved physical volume is $\phi\int h\,dx=V$.